The Fermi - Pasta - Ulam - Tsingou chain_Questions

Please ask your questions below by directly editing the page

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You can insert math formulæ using LaTeX code: e.g. typing

[[math]]
\pi_C(t+1)=\sum_{C'} \pi_{C'}(t) p_{C' \to C}
[[math]]

yields:
$\pi_C(t+1)=\sum_{C'} \pi_{C'}(t) p_{C' \to C}$

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Questions and Remarks:

• Q: It seems to me that the first question may be misleading: "the modes of strictly positive energy for the system" means the modes whose energy cannot be equal to or lower than zero regardless of the initial conditions, right?
• A: The modes are the Fourier modes which are defined in the text. You have to determine their energies, and determine how many of them have a strictly positive energy.
• Q: The equation admits wave solutions only with positive velocities, therefore for me the interaction of waves with "opposite velocities" is impossible, I'm missing something?
• A: Don't forget the role of the initial state!